I wish that it was possible to see how much damage you did with each hit. Its possible to do this if you get sacrificed, so why not have an option to see this while being alive as well?
If you play Alice's Maze up to floor 6, you get around 350-400 faction points, and it takes maybe around 20-30 minutes depending on how good/powerful the people your playing with are. Under those conditions, it shouldnt take super long time to get all those trophies. Doing normal missions only, where you get like 5 or 10 faction points for each round, that would take ages indeed..